Kelvin Water Dropper experiment refers to the electrostatic generator invented by Lord Kelvin, which uses falling water to generate a voltage by electrostatic induction occurring between interconnected, oppositely charged systems.
The way I have heard it explained is not by the container but the water drops themselves. Statistically there is no way you can get a perfectly neutral water drop every single time. Eventually you will get a drop with a charge of 0.000000001 coulombs. This tiny imbalance is enough to set the experiment in motion into a positive feedback system.
You can think about it this way, imagine a factory that makes steel balls that have a mass of 100 grams each. Is it reasonable to think that every single ball from the factory will have a mass of exactly 100 grams and not vary to even 100.0000000000000000001 grams? Electrical charge functions the same way. No macro size object has a perfectly neutral charge. Even the earth ground in circuits has a charge, it is just that the actual charge is so insignificant that you can almost always consider the ground potential to be 0V.